The halting problem is unsolvable due to a contradiction, but there is a finite set of programs with given number of symbols; one or more of them share the max non infinite running time, and if you did have the oracle to answer that, you can in fact run the algorithm provided, except for how long this would take in real time.
A different take is that you can write a program that will only terminate if ZF set theory is false, which is impossible to prove using math due to Gödel's incompleteness theorems. We assume this program should run forever, but would not be able to prove it. That program provides some upper bound to the highest BB number we could ever hope to prove with certainty: 748 according to this article from a few years back.
The problem of the post is that an all knowing oracle doesn’t have this problem, and assuming the program has finite length, our being able to prove whether it halts or not does not stop there from being an answer to that question.
https://www.quantamagazine.org/the-busy-beaver-game-illumina...